Q1) The midpoints of the adjacent sides of a triangle are joined. The midpoints of the adjacent sides of the resultant triangles are also joined.The ratio of the area of the central small triangle to the original triangle is:
a) 1 : 4
b) 1 : 8
c) 1 : 12
d) 1 : 16
e) 1 : 24

Q3) In a locality, there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other?
a. 56
b. 73
c. 80
d. 120
e. None of the above

Q5) A container has 100 liters (mixture of milk and water) in the ratio of 3:2. When 40 liters of mixture is taken out and replaced with the same amount of water, what is the ratio of milk and water left in the container?

Q6) Samyak’s wrist watch lagged behind by 12 min on Thursday at 6:00 am while it was 16 min ahead on Saturday at 9:00 pm in the same week. At what time did the watch show the correct time?
a. 9 pm on Friday
b. 9 am on Friday
c. 1:30 pm on Friday
d. 12:30 am on Saturday
e. None of the above

Q7) A 25 ft long ladder is placed against the wall with its base 7 ft the wall. The base of the ladder is drawn out so that the top comes down by half the distance that the base is drawn out. This distance is in the range:
a. (2, 7)
b. (5, 8)
c. (9, 10)
d. (3, 7 )
e. None of the above

Q19) A positive integer n has exactly 4 positive divisors that are perfect fifth powers, exactly 6 positive divisors that are perfect cubes, and exactly 12 positive divisors that are perfect squares. Find the least possible number of possible integers that are divisors of n